The thing about the PT is that we know this is Anakin Skywalker's story arc.

Well, we don't actually, not if we're watching the films in chronological order. One of the goals of many PT fanedits (including, I believe, Adywan's Revisited series) is to make them viewable in chronological order without spoiling the plot twist in ESB. To argue that we already know all this because we wouldn't be sitting here editing the films otherwise is missing the point; if TPM is designed to be the first seen in the sequence, as GL claims and several fanedits are designed, it's OK if it stands alone and sets up the universe and we don't really hit the "main" plot (which does tie into the events of TPM; we must remember that it's in TPM that Palpatine gets elected Chancellor) until AOTC.

Re Ady's PT nods in ANH:R, they make sense on the above theory because it's ultimately going to be the fourth film in the sequence, so it has to tie in more; although it's still going to follow a time skip so it has to start afresh to some extent.